If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x) = f(x) g(x).

−9
−24
0
24

Question

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x) = f(x) g(x).

 −9
 −24
 0
 24

zepdrix · Answer

Oh these are always fun :)
Application of the chain rule.
Chain rule is the most difficult of the simple derivative rules.
So spend a lot of time on it!!!

zepdrix · Answer

Oh this is actually product rule, my bad haha :D

zepdrix · Answer

$$\large\rm h(x)=f(x)g(x)$$Our product rule tells us that$$\large\rm h'(x)=f'(x)g(x)+f(x)g'(x)$$

anonymous · Answer

i got that part

zepdrix · Answer

Ok cool :)

Evaluating h'(x) at x=1 gives us:$$\large\rm h'(\color{orangered}{1})=f'(\color{orangered}{1})g(\color{orangered}{1})+f(\color{orangered}{1})g'(\color{orangered}{1})$$

zepdrix · Answer

They didn't give you g'(1)? 0_o
whut?
What is this madness? Hmm interesting..

zepdrix · Answer

Oh oh, they did.
They gave you extra stuff.. I see

anonymous · Answer

yeah it confused me because it gave 2 g'

zepdrix · Answer

That might make things a little confusing.
They gave you `6 pieces of information`.
You only need 4 of those.

anonymous · Answer

so i would do h'(1)=(4)(-3) + (3)(-4)?

anonymous · Answer

-12-12=-24?

zepdrix · Answer

Mmm yes that looks right!

anonymous · Answer

yay! thanks

zepdrix · Answer

:D